Royal Society. 219 



composing a multitude of minute prisms, growing, as if by a species 

 of vegetation, and variously arranged in sprigs and branchlets, often 

 resembling in miniature, the tufts of marine confervae. A similar 

 plumose appearance, accompanied with the same analytic proper- 

 ties, is obtained from the evaporation of a drop of a mixed solution 

 of nitre and gum arable. This analytic effect is shown to be the 

 consequence of the high degree of doubly refractive power pos- 

 sessed by these crystalline filaments, and which exists even in those 

 whose diameter is evanescent on microscopic examination. The 

 author entertains hopes that it will be possible to obtain large and 

 permanent artificial crystals, which may possess the advantages of the 

 tourmaline, without the inconvenience resulting from its dark colour. 



December 22, 1836 — '* First Memoir on the Theory of Analy- 

 tical Operations." By the Rev. Robert Murphy, M.A., F.R.S., 

 Fellow of Caius College, Cambridge. 



The author considers the elements of which every distinct analy- 

 tical process is composed, as of three kinds; the first, being the 5m6- 

 jecty that is, the symbol on which a certain notified operation is to 

 be performed; the second, the operation itself, represented by its 

 own symbol; and the third, the result ^ which may be connected with 

 the former two by the algebraic symbol of equality. The operations 

 are either wowoww/ or polynomial', simple or compounds and with 

 respect to their order, are e\\\\QV fixed ox free. He uses the term 

 linear operations to denote those of which the action on any subject 

 is made up by the several actions on the parts, connected by the 

 signs plus or minus^ of which the subject is composed ; and these 

 linear operations likewise may be monomial or polynomial. 



A variety of theorems for the development of functions of a very 

 general nature are then deduced from expansions of the fundamen- 

 tal expressions, derived from the principles stated in the beginning 

 of this memoir : and various laws embracing the relations subsisting 

 between analytical operations, and the fundamental formulae for their 

 transformation are investigated. 



*' Observations and Experiments on the Solar Rays that occasion 

 Heat ; with the application of a remarkable property of these rays 

 to the construction of the Solar and Oxy-hydrogen Gas Micro- 

 scopes." By the Rev. J. B. Reade. Communicated by J. G. ChiU 

 dren, Esq., Sec. R.S.* 



The method employed by the author for obtaining, by a com- 

 bination of lenses, the convergence to foci of the colorific solar rays, 

 together with the dispersion of the calorific rays, consists in making 

 a beam of solar light, which contains both kinds of rays, pass, after 

 it has been converged to a focus by a convex condensing lens, 

 through a second convex lens, placed at a certain distance beyond 

 that focus: that distance being so adjusted as that the calorific rays, 

 which, from their smaller refi'angibility, are collected into a focus 

 more remote from the first lens than the colorific rays, and conse- 

 quently nearer to the second lens, shall, on emerging from the 

 latter, be either parallel or divergent j while the colorific rays, which, 



* See our present Number, p. 184. 

 2 F2 



